WO 00/58914 describes a percept-response system based on channel representation of information. A link matrix C links a feature vector a, which has been formed from a measured percept (column) vector x, to a response (column) vector u using the matrix equation:u=Ca  (1)
A fundamental consideration in these systems is system training, i.e., how to determine the linkage matrix C. In WO 00/58914 this is accomplished by collecting different training sample pairs of feature vectors ai and response vectors ui. Since each pair should be linked by the same linkage matrix C, the following set of equations is obtained:
                                                        U              =                            ⁢                              (                                                                                                    u                        1                        1                                                                                                            u                        1                        2                                                                                    ⋯                                                                                      u                        1                        N                                                                                                                                                u                        2                        1                                                                                                            u                        2                        2                                                                                    ⋯                                                                                      u                        2                        N                                                                                                                        ⋮                                                              ⋮                                                              ⋮                                                              ⋮                                                                                                                          u                        K                        1                                                                                                            u                        K                        2                                                                                    ⋯                                                                                      u                        K                        N                                                                                            )                                                                                        =                            ⁢                                                (                                                                                                              c                          11                                                                                                                      c                          12                                                                                            ⋯                                                                                              c                                                      1                            ⁢                            H                                                                                                                                                                                        c                          21                                                                                                                      c                          22                                                                                            ⋯                                                                                              c                                                      2                            ⁢                            H                                                                                                                                                              ⋮                                                                    ⋮                                                                    ⋮                                                                    ⋮                                                                                                                                      c                          K1                                                                                                                      c                          K2                                                                                            ⋯                                                                                              c                          KH                                                                                                      )                                ⁢                                  (                                                                                                              a                          1                          1                                                                                                                      a                          1                          2                                                                                            ⋯                                                                                              a                          1                          N                                                                                                                                                              a                          2                          1                                                                                                                      a                          2                          2                                                                                            ⋯                                                                                              a                          2                          N                                                                                                                                    ⋮                                                                    ⋮                                                                    ⋮                                                                    ⋮                                                                                                                                      a                          H                          1                                                                                                                      a                          H                          2                                                                                            ⋯                                                                                              a                          H                          N                                                                                                      )                                                                                                        =                            ⁢              CA                                                          (        2        )            where N denotes the number of training samples or the length of the training sequence and A is denoted a feature matrix. These equations may be solved by conventional approximate methods (typically methods that minimize mean squared errors) to determine the linkage matrix C (see for example Using MATLAB, MathWorks Inc, 1996, pp. 4-2-4-3, 4-13-4-14). However, a drawback of these approximate methods is that they restrict the complexities of associative networks to an order of thousands of features and thousands of samples, which is not enough for many systems.